Use of coefficient of a power curve to evaluate a semiconductor wafer

ABSTRACT

A coefficient of a function that relates a measurement from a wafer to a parameter used in making the measurement (such as the power of a beam used in the measurement) is determined. The coefficient is used to evaluate the wafer (e.g. to accept or reject the wafer for further processing), and/or to control fabrication of another wafer. In one embodiment, the coefficient is used to control operation of a wafer processing unit (that may include, e.g. an ion implanter), or a heat treatment unit (such as a rapid thermal annealer).

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is related to and incorporates by reference herein inits entirety, the commonly owned, copending U.S. patent application Ser.No. 09/544,280, attorney docket [M-5439-2C US], filed Apr. 6, 2000,entitled “Apparatus And Method For Evaluating A Semiconductor Wafer” byPeter G. Borden et al., which is a continuation of Ser. No. 09/095,804,attorney docket [M-5439 US], filed Jun. 10, 1998 now issued as U.S. Pat.No. 6,049,220.

This application is also related to and incorporates by reference hereinin its entirety the commonly owned, copending U.S. patent applicationSer. No. 09/274,821, attorney docket [M-7045 US] filed Mar.22, 1999,entitled “Apparatus And Method For Determing The Active Dopant ProfileIn A Semiconductor Wafer,” by Peter G. Borden et al.

BACKGROUND OF THE INVENTION

In the processing of a semiconductor wafer to form integrated circuits,charged atoms or molecules are directly introduced into the wafer in aprocess called ion implantation. Ion implantation normally causes damageto the lattice structure of the wafer, and to remove the damage, thewafer is normally annealed at an elevated temperature, typically 600° C.to 1100° C. Prior to annealing, material properties at the surface ofthe wafer may be measured, specifically by using the damage caused byion implantation.

For example, U.S. Pat. No. 4,579,463 granted to Rosencwaig et al. (thatis incorporated herein by reference in its entirety) describes a methodfor measuring a change in reflectance caused by a periodic change intemperature of a wafer's surface (see column 1, lines 7-16).Specifically, the method uses “thermal waves [that] are created bygenerating a periodic localized heating at a spot on the surface of asample” (column 3, lines 54-56) with “a radiation probe beam . . .directed on a portion of the periodically heated area on the samplesurface,” and the method “measures] the intensity variations of thereflected radiation probe beam resulting from the periodic heating”(column 3, lines 52-66).

As another example, U.S. Pat. No. 4,854,710 to Opsal et al. (alsoincorporated herein by reference in its entirety) describes a methodwherein “the density variations of a diffusing electron-hole plasma aremonitored to yield information about features in a semiconductor”(column 1, lines 61-63). Specifically, Opsal et al. state that “changesin the index of refraction, due to the variations in plasma density, canbe detected by reflecting a probe beam off the surface of the samplewithin the area which has been excited” (column 2, lines 23-31) asdescribed in “Picosecond Ellipsometry of Transient Electron-Hole Plasmasin Germanium,” by D. H. Auston et al., Physical Review Letters, Vol. 32,No. 20, May 20, 1974.

Opsal et al. further state (in column 5, lines 25-31 of U.S. Pat. No.4,854,710): “The radiation probe will undergo changes in both intensityand phase. In the preferred embodiment, the changes in intensity, causedby changes in reflectivity of the sample, are monitored using aphotodetector. It is possible to detect changes in phase throughinterferometric techniques or by monitoring the periodic angulardeflections of the probe beam.”

A brochure entitled “TP-500: The next generation ion implant monitor”dated April, 1996 published by Therma-Wave, Inc., 1250 Reliance Way,Fremont, Calif. 94539, describes a measurement device TP-500 thatrequires “no post-implant processing” (column 1, lines 6-7, page 2) andthat “measures lattice damage” (column 2, line 32, page 2). The TP-500includes “[t]wo low-power lasers [that] provide a modulated reflectancesignal that measures the subsurface damage to the silicon latticecreated by implantation. As the dose increases, so does the damage andthe strength of the TW signal. This non-contact technique has no harmfuleffect on production wafers” (columns 1 and 2 on page 2). According tothe brochure, TP-500 can also be used after annealing, specifically to“optimize . . . system for annealing uniformity and assure goodrepeatability” (see bottom of column 2, on page 4).

U.S. Pat. No. 5,978,074 discloses focusing a probe beam onto a samplesurface within an area periodically excited by an intensity modulatedgeneration beam. The power of the reflected probe beam is measured by aphotodetector, and the modulated optical reflectivity of the sample isderived. Measurements are taken at a plurality of pump beam modulationfrequencies. In addition, measurements are taken as the lateralseparation between the pump and probe beam spots on the sample surfaceis varied.

At column 3, lines 23-30, U.S. Pat. No. 5,978,074 states that “in theprior art, the modulation range was typically in the 100 KHz to 1 MHzrange. Some experiments utilized modulation frequency as high as 10 MHz.In the subject device, it has been found useful to take measurementswith modulation frequencies up to 100 MHz range. At these highfrequencies, the thermal wavelengths are very short, enablinginformation to be obtained for thin metal layers on a sample, on theorder of 100 angstroms.”

At column 8, lines 22-27, U.S. Pat. No. 5,978,074 further states “Onceall measurements at various spacings and modulation frequencies havebeen taken and stored, the processor will attempt to characterize thesample. Various types of modeling algorithms can ve used depending onthe complexity of the sample. Optimization routines which use iterativeprocesses such as least square fitting routines are typically employed.”

Abruptness of a junction in a semiconductor wafer can be measured bySecondary Ion Mass Spectrometry (SIMS) in which a wafer is milled awayusing an ion beam, and the removed material is analyzed. Alternatively,abruptness of a junction can also be determined from electricalcharacteristics of transistors or other test structures on a completelyfabricated integrated circuit (IC) device, having contacts.

SUMMARY

An apparatus and method in accordance with the invention use a computerto determine a coefficient in a function that relates measurements froma wafer, to values of a parameter used in making the measurements, anduse the coefficient to evaluate the wafer (e.g. to accept or reject thewafer for further processing), and/or to control fabrication of anotherwafer. For example, the apparatus and method may use a second ordercoefficient of a power series function to control operation of a waferprocessing unit (that may include, e.g. an ion implanter), or a heattreatment unit (such as a rapid thermal annealer).

In one embodiment, two beams are used to make measurements that areinput to the computer: one beam (called “generation beam”) of photonshaving an intensity modulated at a frequency sufficiently low to avoidcreation of a wave of charge carriers in the wafer, and another beam(called “probe beam”) used to measure the concentration of chargecarriers created by the generation beam. Specifically, a photosensitiveelement located in a path of a portion of the probe beam that isreflected by the charge carriers (and that is therefore also modulated)generates an electrical signal indicative of the concentration. Suchmeasurements are related by the above-described function to theabove-described parameter (which may be, for example, power of thegeneration beam, power of the probe beam, or spot size).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates, in a high level block diagram, a system includingan apparatus (called “active dopant profiler”) in accordance with theinvention.

FIG. 1B illustrates, in a flow chart, acts performed by the system ofFIG. 1A.

FIG. 2A illustrates, in a flowchart, the acts performed by the system ofFIG. 1A in one implementation.

FIG. 2B illustrates, in a graph, the temporal modulation of chargecarriers by the active dopant profiler of FIG. 1A, without creation of awave, in a critical aspect of one embodiment.

FIG. 2C illustrates, in a flowchart, creation of charge carriers by useof a generation beam.

FIG. 2D illustrates, in a cross-sectional view, use of a probe beam anda generation beam, each beam focused coincident with the other by theactive dopant profiler of FIG. 1A.

FIGS. 2E and 2F illustrate, in graphs, variation of a measurement ofintensity of a portion of the probe beam reflected by the wafer of FIG.1A, as a function of a piezoelectric voltage that controls the distancebetween the two beams of FIG. 2D along axis x (FIG. 2E) and axis y (FIG.2F), the two axes being illustrated in FIG. 2H.

FIGS. 2G and 2H illustrate, in a cross-sectional view and a plan viewrespectively, beams 151 and 152 of FIG. 2D offset from each other, (andalso superimposed in the view of FIG. 2G is a graph of the concentration164 of excess charge carriers as a function of the distance from axis161 of generation beam 151).

FIG. 2I illustrates, in a plan view, beams 151 and 152 separated fromeach other.

FIG. 2J illustrates, in a flow chart, the acts performed by computer103C of FIG. 1A to use a coefficient of a power curve in evaluating awafer.

FIG. 3A illustrates, in a graph, intensity measurements (made by theprofiler of FIG. 1A) plotted along y axis as a function of power of thegeneration beam for three wafers, wherein the intensity measurementshave been normalized.

FIG. 3B illustrates in a graph, change in curvature (along the y axis)of the power curves of FIG. 3A as a function of anneal temperature(along the x axis).

FIG. 4 illustrates a graph used to convert curvature (along the x axis)obtained from measurements into anneal temperature (along the y axis).

FIG. 5 illustrates, in a block diagram, various components used in oneimplementation of the active dopant profiler of FIG. 1A.

DETAILED DESCRIPTION

In accordance with the invention, an apparatus and method measure (in afirst act) intensity of a beam reflected by charge carriers in thesemiconductor material, change (in a second act) a parameter thataffects the charge carriers, and repeat the measuring act 1, to obtain anumber of measurements for a corresponding number of values of theparameter. Thereafter, the apparatus and method determine (in a thirdact) a coefficient of a function (such as a power series) that relatesthe measurements to the parameter values. Depending on the embodiment,the coefficient being determined can be of any order, such as secondorder (i.e. of a quadratic term), first order (i.e. of a linear term),and/or zeroth order (i.e. a constant).

In one embodiment, a second order coefficient is used as an indicator ofabruptness of a junction in the wafer, and is used to control formationof the junction in another wafer and/or to accept/reject thejust-fabricated wafer. In other embodiments, the zeroth order and/or thefirst order coefficients are used. to control annealing of anotherwafer. The first order coefficient is indicative of the junction depth,which depends on the annealing temperature. The annealing temperaturecan affect the abruptness, and, hence, the second order coefficient aswell.

In one implementation, the apparatus and method use two beams, a firstbeam to create charge carriers, and a second beam to measurereflectivity due (at least in part) to the charge carriers. The chargecarriers (also called “excess carriers”) being created by the first beamare in excess of a number of charge carriers (also called “backgroundcarriers”) that are normally present in the wafer in the absence ofillumination. In this embodiment, additional charge carriers (alsocalled “measurement-related carriers”) due to incidence of the secondbeam (also called “probe beam”) are minimized or avoided, although inother embodiments such measurement related carriers are also used (e.g.to bias the junction, and a signal is measured, for different powers ofprobe beam).

Depending on the implementation, intensity of the first beam (alsocalled “generation beam”) can be modulated, at a frequency sufficientlylow to avoid creation of a wave of charge carriers in the wafer when thefirst beam is incident on the wafer. Depending on the energy carried bysuch a wave, the wave perturbs the carrier distribution and diminishesthe physical effect that makes the measurements (in the first actdescribed above) a function of the parameter being changed (in thesecond act also described above.), e.g. makes charge carrier reflectancev/s power of generation beam a function of depth and abruptness. Themodulation of the first beam is used primarily to detect very smallsignal using a lock-in amplifier.

Also, if both beams are laser beams, photons of the first beam and ofthe second beam may be respectively selected to have energy greater thanand less than the bandgap energy of semiconductor material in the wafer.When two beams are used, centers of the two beams may be separated from(e.g. by 1 micron or more) or coincident with one another, depending onthe embodiment. When the beams are separated from one another, thedistance of separation can be either fixed, or variable, also dependingon the embodiment, as long as the effect of a wave of charge carriers isminimized or eliminated from the measurements used as described hereinto evaluate a semiconductor wafer.

Also, the beams may have spots that overlap or spots that are completelyseparated from one another, again depending on the embodiment. Insteadof using the just-described first beam, any other mechanism well knownin the art may be used to change the number of charge carriers thatreflect the second beam. Also depending on the embodiment, measurementsof the type described herein can be done with or without variation ofthe distance between the two beams. As noted elsewhere herein,measurements of one embodiment are made with the distance between twobeams kept fixed for all measurements.

The apparatus and method of one implementation use a photosensitiveelement located in a path of a portion of the second beam reflected bythe charge carriers, to generate an electrical signal related toreflectivity due to the charge carriers. Depending on theimplementation, the photosensitive element may be located directly insuch a path, or may be part of an interferometer that is located in sucha path. The interferometer may be used to measure interference between aportion of the second beam reflected by charge carriers in the wafer,and one of: (1) another portion of the second beam that is reflected bythe front surface of the wafer, or (2) a reference beam that has atime-varying phase but is coherent with the second beam reflection fromthe charge carriers.

In another implementation, the apparatus and method interfere areflected portion of the second beam with an un-reflected portion of thesecond beam to obtain a sum component and a difference component, anddetermine a difference between the sum component and the differencecomponent. In yet another implementation, the apparatus and methodinterfere a reference beam with the second beam portion reflected by thecharge carriers and also interfere the reference beam with the secondbeam portion reflected by the wafer's front surface, and measure thephase difference between the two interference signals.

Between measurements, the apparatus and method of one implementationchange the average number of charge carriers, so that the correspondingelectrical signal being measured also changes. A computer coupled to thephotosensitive element (either directly or indirectly e.g. through alock-in amplifier and/or through an interferometer), is programmed todetermine one or more coefficients (such as the second ordercoefficient) of a power series function that relates the electricalsignal to the measurement.

In the above-described implementation, the computer relates changes inthe intensity (also called “power”) of the first beam to correspondingchanges in the electrical signal, and the resulting function is referredto as a “power curve.” The computer is programmed to determine thecurvature of such a power curve, and use the curvature to extractmeasured values of physical parameters such as junction abruptness, andto accept/reject the current wafer, and/or to control fabrication ofanother wafer. Depending on the implementation, the computer may beoptionally programmed to normalize the measurements prior to determiningthe curvature of the power curve, e.g. so that sensitivity to otherparameters is reduced. Normalization may be used to eliminatesensitivity to, e.g. reflectivity of the surface of the semiconductor,although in another embodiment there is no normalization.

The computer may include a memory having encoded therein correspondingvalues of the coefficient that have been determined from wafers havingknown properties. If so, the computer uses the stored values to identifyone or more properties of the wafer being tested (e.g. uses the secondorder coefficient to look up abruptness). Alternatively, the computermemory may have encoded therein one or more limits that are comparedwith the value of the coefficient for the wafer being tested, todetermine a change (if any) that is to be made in operation of the heattreatment unit or the ion implantation unit (or both) so that thecorresponding coefficient for a to-be-fabricated wafer falls within thelimits.

A wafer fabrication system 100 (FIG. 1A) in one embodiment createsintegrated circuit (abbreviated as “IC”) dice by processing a wafer toform a “patterned wafer”, measuring a material property of the patternedwafer, and adjusting the processing in real time if necessary, to obtainimproved properties in a wafer fabricated next (or in a subsequentlyfabricated wafer, depending on the speed of measurement). Thejust-described processing can include annealing, and the measurement ofa material property can be performed on a patterned wafer afterannealing, thereby to determine process conditions not obtainable byprior art methods, e.g. to determine anneal temperature frommeasurements on the annealed wafer.

Measurement on patterned wafers during fabrication as described hereineliminates test wafers that may be otherwise required in the prior artsolely to monitor the fabrication process, thus reducing costs.Moreover, measurements on annealed wafers as described herein provide ameasure of one or more properties that are related to the electricalcharacteristics (such as processing speed) of the devices beingfabricated, because annealing results in activation of the dopants usedin the devices.

A wafer 104 is processed by a system 100 that includes a waferprocessing unit 101 and an annealer 102 used to fabricate (see operation120 in FIG. 1B) a portion thereof. A wafer in any stage of fabrication,such as one of wafers 104, 105 and 106 may be evaluated by a measurementdevice (hereinafter “active dopant profiler” or “profiler”) 103 (FIG.1A). Therefore, in the following description, the notation “104/105/106”is used to indicate that the description is equally applicable to eachof wafers 104, 105 and 106. Similarly the notation “105/106” indicateseach of wafers 105 and 106.

Specifically, a profiler 103 in accordance with the invention measures(see operation 140 in FIG. 1B) a property of wafer 104/105/106, changes(see act 150) a parameter related to charge carriers, and repeats themeasurement act. Operation 140 and act 150 may be repeated n times (e.g.10 times) to obtain a corresponding number of measurements. Next, in act160, a programmed computer 103C in profiler 103 determines a coefficientof a function that relates the measurements to the values of theparameter, e.g. by curve fitting. In one embodiment, computer 103Cdetermines the second order coefficient (i.e. also called “curvature”)of a power series function, although in other embodiments, othercoefficients of such a function or of other functions are determined.

Next, in act 170, computer 103C uses the just-described coefficient as ameasure of a semiconductor property of wafer 104/105/106. For example,computer 103C uses the second order coefficient as a measure of theabruptness of a junction in the wafer 104/105/106. In other examples,computer 103C uses the first order coefficient (also called “slope”)and/or the zeroth order coefficient (also called “constant”) of thefunction as a measure of anneal temperature and/orjunction depth.

Measuring junction abruptness as described above is non-destructive, andcan be used on patterned wafers immediately after junction formation. Inaddition, such a measurement takes just a few seconds, and provides thethroughput required for process control applications. Moreover, themethod provides an unexpected result, considering that at least oneprior art reference, namely U.S. Pat. No. 4,854,710 granted to Opsalteaches that depth information cannot be obtained in the absence of aplasma wave (specifically, Opsal states in column 4, lines 33-35,“[h]owever, in applications where sample variations as a function ofdepth need to be studied, it is necessary to generate and study plasmawaves”).

In one embodiment, system 100 performs an operation 120 (FIG. 1B) e.g.by operating an ion implanter 101I to create (as illustrated by act 121of FIG. 2A), in a wafer 104 (FIG. 1A), one or more regions that havedopant atoms (e.g. boron atoms in silicon). Instead of ion implantation,any other process for creating doped regions, e.g. chemical vapordeposition, epitaxial deposition, evaporation, diffusion, or plasmadeposition can be used in unit 101 (FIG. 1A) to perform act 120. Suchregions may have a junction that is, for example less than 100 nm thick,and may even be less than 50 nm thick.

Thereafter, a patterned wafer 105 having one or more patterns of dopedregions is transferred to a rapid thermal annealer 102 (FIG. 1A) thatmay be included in system 100. Rapid thermal annealer (also called“annealer”) 102 performs an annealing act 122 (FIG. 2A), e.g. by heatingwafer 105 (FIG. 1A) to a predetermined temperature (also called“annealing temperature”), e.g. to remove damage that is normally causedby ion implanter 101 to the lattice structure of the semiconductormaterial in the doped regions of wafer 105. Instead of a rapid thermalannealer, a furnace may be included in system 100 and used to annealwafer 105 in act 122 (FIG. 2A).

Annealing in act 122 causes the dopant atoms (also called “dopants”) tomove into the lattice of the semiconductor material in a doped region,where the dopants act as donors (forming n-type material) or acceptors(forming p-type material). The extent to which the dopants incorporateinto the lattice structure during act 122 is a function of thetemperature at which and the time for which act 122 is performed. Theincorporation is more complete at a higher temperature or after a longertime.

However, the dopants also diffuse (i.e. move) during act 122, therebyincreasing the junction depth. The diffusion proceeds more rapidly at ahigher temperature, and it is necessary to carefully control theannealing temperature. Therefore, abruptness of the junction is measuredafter act 122 (wherein wafer 104/105/106 is positioned within profiler103), and the abruptness is compared with predetermined information(e.g. a specified limit or abruptness of wafers known to be good) todetermine a change (if any) to be made to the annealing process and/orion mplantation process. Dynamic feedback of such to-be-made changes tothe fabrication operation in real time as described herein improves theyield of good wafers obtained from fabrication in a manner not otherwisepossible in the prior art.

In one embodiment, an annealed wafer 106 (FIG. 1A) is transferred fromrapid thermal annealer 102 to profiler 103, and positioned therein (seeact 123 in FIG. 2A). In an alternative embodiment, an active dopantprofiler is integrated into a rapid thermal annealer and does notrequire positioning after completion of anneal. In one embodiment,profiler 103 is moved relative to wafer 106 instead of moving wafer 106.

As noted above, a non-annealed wafer 105 can also be used (moved viapath 109 in FIG. 1A) e.g. if dopant regions do not require annealing dueto use of a method other than ion implantation, such as diffusion(wherein dopants are diffused into wafer 105 thermally, and are active,and there is no need to anneal out implant damage, or where dopant atomsare grown into the semiconductor through a process such as chemicalvapor deposition (CVD)). Profiler 103 evaluates the efficacy of thedopants in a non-annealed wafer 105 in a manner similar to thatdescribed above for annealed wafer 106. A starting wafer 104 can also beused as illustrated by a path 112 in FIG. 1A.

Next, after a wafer 104/105/106 is properly positioned, profiler 103creates (see act 130 in FIG. 2A) in a region of the wafer, a number ofexcess charge carriers that are modulated at a predetermined frequency.The predetermined frequency is selected to ensure that a wave of thecharge carriers is not created during the measurement (see operation 140in FIG. 2A). As profiler 103 does not use a “plasma wave” as describedin U.S. Pat. No. 4,854,710, profiler 103 is as effective in measuring aproperty of an annealed wafer 106 as in measuring a property of anon-annealed wafer 104/105.

Prior to measuring a material property in operation 140, profiler 103creates (see act 130 in FIG. 2A), in a region 128 (FIG. 2B) of wafer104/105/106, a concentration n_(e) of excess carriers, and modulatesconcentration n_(e) (i.e. increases and decreases) as a function of timet but not as a function of distance x, e.g. from a central axis 155(FIG. 2B) of region 128. Specifically, over a time period that is theinverse of the modulation frequency, profiler 103 changes concentrationn_(e) between the values n_(ea)-n_(en), whereinn_(en)≦n_(ej)≦n_(ei)≦n_(ea) (FIG. 2B). Therefore, at any given time ti,the value n_(ei) of the carrier concentration decays as a function ofthe distance x, without the creation of a wave in space. Profiler 103 ofone embodiment ensures that there is no periodicity in space of thevalue of concentration n_(e). Instead, concentration n_(e) simply decaysradially (e.g. roughly exponentially as a function of radial distance)outside region 128, as illustrated in FIG. 2B.

To ensure the absence of a wave in space, the frequency of modulation ofcarrier concentration C is selected to be several times (e.g. one ormore orders of magnitude) smaller than the modulation frequencies usedin the prior art to generate waves as described in, for example, U.S.Pat. No. 4,854,710. Specifically, in one implementation of thisinvention, the modulation frequency is approximately 1 KHz that is onethousand times (three orders of magnitude) smaller than a 1 MHzfrequency described in column 15, line 18 of U.S. Pat. No. 4,854,710 byOpsal. Use of such a low modulation frequency is a critical aspect inone embodiment, and leads to unexpected results due to the eliminationof a wave in space, such as the “wave” described by Opsal. In anotherembodiment, the modulation frequency is any frequency lower than 1000Khz (e.g. 900 Khz) and profiler 103 still provides a measure of amaterial property as described herein.

In one embodiment, profiler 103 implements the above-described act 130(FIG. 2A) by: generating (act 131 in FIG. 2C) a beam 151 (FIG. 2D) ofphotons that have energy greater than the bandgap energy of thesemiconductor material in doped region 138 (FIG. 2D), modulating (act132 in FIG. 2C) beam 151 at a frequency selected to avoid the creationof a wave (as described above), and focusing (act 133 in FIG. 2C) beam151 on doped region 138. Depending on the implementation, beam 151 canhave a spot size (diameter at the wafer's surface) of about 2 microns.

Depending on the implementation, profiler 103 modulates the intensity ofgeneration beam 151 at any frequency in the range of 1 Hz to 20,000 Hz,as described in U.S. patent application Ser. No. 09/544,280 incorporatedby reference above. The modulation frequency can be, for example, 1000Hz, and may require at least 10 cycles for a lock-in amplifier togenerate a reflectance measurement (based on a probe beam as describedbelow in reference to acts 142 and/or 143 of FIG. 2A), or 10milliseconds to perform each reflectance measurement.

Note that frequencies greater than 20,000 Hz can be used, as long as theeffects of a wave are minimized or eliminated (e.g. by use of multiplemodulation frequencies followed by filtering to eliminate the effect ofa change in frequency). Moreover, frequencies lower than 1000 Hz mayalso be used, although use of such low frequencies affects the speed atwhich the measurements are made. In one example, the throughput is 30wafers per hour, or 120 seconds per wafer, with each wafer having ameasurement taken at least ten times in a single region 128, atdifferent power levels. The ten measurements constitute a power curve inthis example. As the abruptness measurement requires several reflectancemeasurements (e.g. requires a number of reflectance measurements foreach of a corresponding number of average carrier concentrations),profiler 103 takes several seconds (e.g. 10 seconds) for each wafer104/105/106. Hence, the 10 millisecond speed of reflectance measurementper power level allows for real time control in the fabrication ofwafers by system 100 (FIG. 1A), using method 200 (FIG. 2A).

Although generation beam 151 is modulated, probe beam 152 is operatedcontinuously at constant power (without modulation). The just-describedact of modulating only one of beams 151 and 152 allows separation inmeasurement of two reflectances: a reflectance caused by the excesscarriers from the background reflectance, since the former changes atthe modulation frequency and can be detected in a synchronous manner bya lock-in amplifier.

In another implementation of act 130, instead of using beam 151 ofphotons, profiler 103 uses a beam of charged particles, such aselectrons or ions. The beam of charged particles is modulated andfocused in the same manner as that described above in reference to beam151 to generate the charge carriers in doped region 138. Instead of abeam of photons or a beam of electrons, any other mechanism (such as acombination of photons and electrons) can be used to create chargecarriers in act 130 (FIG. 2A).

Next, in operation 140, profiler 103 (FIG. 1A) measures a property thatis affected by charge carriers present in doped region 138 in a wafer105/106. In one implementation, profiler 103 measures the reflectancethat is thereafter used to determine one or more properties such asanneal temperature, junction depth, and abruptness. In act 140, insteadof the reflectance, profiler 103 can measure other properties affectedby the created charge carriers, such as the refractive index.

Specifically, one implementation of profiler 103 generates and focuses(see act 141 in FIG. 2A) on a region (also called “illuminated region”)128 illuminated by beam 151, another beam 152 (FIG. 2D) that is used todetect the number of charge carriers in wafer 104/105/106 whenilluminated by beam 151. In one embodiment, probe beam 152 containsphotons having energy lower than the bandgap energy of the semiconductormaterial in illuminated region 128. Such a probe beam 152 avoids thecreation of measurement-related carriers when beam 152 is incident onilluminated region 128, thereby to maintain the charge carrierconcentration the same prior to and during measurement (see acts 142and/or 143 in FIG. 2A) of a property as described below.

Next, profiler 103 measures (see act 142 in FIG. 2A) the intensity of areflected portion of beam 152 (FIG. 2D) that is modulated at thefrequency of modulation of the charge carriers in illuminated region128. The intensity measurement provides an indication of an averageconcentration n_(av) of charge carriers in doped region 138 near surface153 (FIG. 2D), wherein the average concentration n_(av) is a root meansquare average that is measured over the period of one (or more)modulation cycle(s) at the modulation frequency of generation beam 151.A number of such concentration measurements n_(av) in turn indicate,under certain conditions as discussed below, a material property, e.g.the abruptness of a junction in doped region 138. Specifically, in act150, a parameter used in creating charge carriers in act 130 is changed,e.g. the power of beam 151 is changed, and act 142 is repeated, therebyto yield n measurements.

Instead of measuring intensity of beam 152 reflected by the chargecarriers directly (as illustrated by act 142), in another embodiment,intensity of an interference of the reflected portion of beam 152 ismeasured (see act 143 in FIG. 2A). Interference of the reflected portionof beam 152 can be with (1) another portion of beam 152 that isreflected by the front surface of the wafer, or (2) a reference beamthat has a time-varying phase. Interference of the reflected portion ofbeam 152 can also be with an un-reflected portion of beam 152, so as toobtain a sum component and a difference component, and a differencebetween the sum component and the difference component is used as ameasurement. In yet another implementation, the portion of beam 152reflected by the charge carriers (which varies at the modulationfrequency) is interfered with one portion of a reference beam, and theportion of beam 152 reflected by the front surface (which is steady andnot varying at the modulation frequency) is interfered with anotherportion of the reference beam, and the phase difference between the twointerference signals is used as a measurement.

Although in FIG. 2D, beams 151 and 152 are illustrated as beingcoincident, with a common axis 155, in another embodiment illustrated inFIG. 2I one of the beams, e.g. probe beam 152, is displaced with respectto the other beam to obtain an intensity measurement, e.g. location ofgeneration beam 151 is changed on performance of one variant of act 244(FIG. 2A). So beams 151 and 152 are separated each from the other asillustrated by a non-zero distance Δx between the respective axes 162and 161 in FIG. 2G.

An intensity measurement obtained in such an offset position (FIG. 2G)of probe beam 152 with respect to generation beam 151 is used to measurevarious properties of the semiconductor material in doped region 138 amanner similar to the measurements obtained from coincident beams (FIG.2D). The measurement obtained in the offset position (FIG. 2G) providesa measure of carrier concentration, because the concentration decayswith distance d from illuminated region 128. Also, the offset is on theorder of the diffusion length in layer 138 (and the diffusion length ison the order of 5 μm in a heavily doped layer).

Note that in one embodiment, the offset is fixed throughout themeasurement process, for multiple measurements in different locations,unlike the process described in U.S. Pat. No. 5,978,074. Depending onthe embodiment, other differences from U.S. Pat. No. 5,978,074 include,for example, use of a modulation frequency that avoids creation of awave (as opposed to use of frequencies greater than 100 kHz), use of afixed beam size throughout the measurement process (as opposed tovariation in beam size) and for multiple measurements in differentlocations, use of monochromatic light (as opposed to use ofpolychromatic light), and use of a photodetector (as opposed to aspectrometer).

Depending on tolerances in alignment, and properties of the beams suchas the diameter and angle of divergence from a central axis, it ispossible for probe beam 152 to be larger in diameter than generationbeam 151 (as illustrated in FIG. 2H). In one embodiment, measurements insuch a configuration are made and used as described herein. Also, in analternative embodiment, measurements at various diameters of beam 151 orbeam 152 or both may be made and used in the absence of generation of awave of charge carriers, as described herein.

In another embodiment, probe beam 152 has a diameter that is smallerthan or equal to the diameter of generation beam 151 and is used toeliminate the effect of lifetime variations on the measurements ofmobility and doping concentration (as described herein). The smallersize of probe beam 152 is achieved (as illustrated in FIG. 2D) byenlarging the diameter and/or the divergence angle of generation beam151, e.g. by moving a lens used to generate beam 151, or choosing a lenssize that creates a smaller collimated beam diameter as emitted from thegeneration laser.

Note that in act 150, instead of changing the power of generation beam151, another embodiment of profiler 103 changes a diameter of beam 151that also changes the concentration of charge carriers in region 128. Insuch an approach (that avoids generation of a wave of charge carriers),profiler 103 overlays the axes of both beams 151 and 152 and starts withprobe beam 152 larger than generation beam 151. Then, profiler 103gradually expands the size of generation beam 151 until beam 151 is aslarge as probe beam 152. During the process, profiler 103 measures thereflectance at each of a number of sizes of the generation beam 151, andplots these measurements to obtain a curved line, followed bydetermining various attributes (e.g. coefficients) for the curved line.Therefore, profiler 103 compares the coefficient values for a region(e.g. through a graph) with coefficient values of regions having knownmaterial properties, thereby to interpolate one or more materialproperties (such as lifetime and/or diffusion length) of the region.Profiler 103 can also change another parameter related to chargecarriers when making such measurements, as would be evident to a personskilled in semiconductor physics in view of the disclosure.

Although in the above-described embodiments, a probe beam 152 havingphotons of energy below the bandgap energy of wafer 156 is used (toavoid the creation of measurement-related carriers during themeasurement), in another embodiment a small percentage (e.g. less than10%) of charge carriers in addition to the charge carriers created bygeneration beam 151 are created by use of a probe beam 152 (samereference numeral is used for convenience) having photons of energy ator slightly above (e.g. 10% above) the bandgap energy. Themeasurement-related carriers created by such a probe beam 152 are in asufficiently small percentage (e.g. an order of magnitude smaller thanthe number created by the generating beam) to provide a reasonablyaccurate measurement of reflectance (e.g. to within 5%).

The overall accuracy of a measurement as described herein is alsogoverned by other inaccuracies involved in the act of measuring, e.g.inaccuracies in a measurement device, such as an amplitude detector.Therefore, in one embodiment the inaccuracy caused by themeasurement-related carriers is kept only as small as necessary tomaintain the overall accuracy below a predetermined limit. Specifically,the percentage of measurement-related carriers is kept sufficientlysmall when the rate per unit volume of the carriers generated bygeneration beam 151 (obtained by dividing the photon flux per unit areaby the absorption length), is at least one order of magnitude (or more)larger than for probe beam 152.

The photon flux per unit area described above is the number of photonsper unit energy obtained by dividing the power P of generation beam 151by the area (πW₀ ²) of illumination by Plank's constant h and the ratioof the speed c of light to the wavelength λ as shown in the followingformula: photon flux=(P/πW₀ ²)×(1/h(c/λ)). The absorption length is thedepth from surface 153 at which the intensity of generation beam 151drops to (1/e) of the intensity at surface 153.

In one implementation, the intensities of beams 151 and 152 are keptapproximately equal (e.g. 100 milliwatts per cm²), and the number ofcharge carriers (also called “measurement-related carriers”) created bybeam 152 is less than 10% of the number of charge carriers (also called“excess carriers”) that are created by generation beam 151 due to thedifference in absorption lengths. Note that in other implementations,beams 151 and 152 can have powers different from each other (e.g. 100milliwatts and 25 milliwatts respectively), and yet maintain the numberof measurement-related carriers at a negligible percentage. For example,probe beam 152 can have photons of energy greater than the bandgapenergy, if the power of probe beam 152 is sufficiently less than thepower of generation beam 151 (to keep the measurement-related carriersat a negligible percentage).

In one implementation, probe beam 152 has a generation rate one or moreorders of magnitude smaller than the generation rate of generation beam151. As noted above, the difference in generation rates is obtained byusing beams 151 and 152 that have different absorption lengths in thesemiconductor material of wafer 156, or by generating beams 151 and 152at different powers or different diameters, or all of the above. Invarious implementations, the pair of beams 151 and 152 are generated byone of the following pairs of lasers: (AlGaAs, InGaAs), (Ar, InGaAs),(NdYAG, InGaAs), and (NdYAG, AlGaAs).

In one or more of the implementations, e.g. for use of lasers (NdYAG,AlGaAs), the power of probe beam's laser (e.g. AlGaAs) is maintainedless than the power of generation beam's laser (e.g. NdYAG) because theabsorption length of the probe beam is a fraction (e.g. one-tenth) ofthe absorption length of the generation beam. In another example, aprobe beam 152 formed by a HeNe laser is maintained at a power less thanor equal to ¼^(th) power of generation beam 151 formed by an Ar laser(having an absorption length 1.2 μm that is ¼^(th) the 3.0 μm length ofthe HeNe laser beam). In the just-described implementation, the power ofthe reflected portion of probe beam 152 is maintained large enough (byhaving a sufficiently large power of probe beam 152) to be detected withsufficient accuracy (e.g. with error of 5% or less) required forreflectance measurements as described herein.

In one variant of this implementation, the difference between thegeneration rates of beams 151 and 152 is one order of magnitude only atsurface 153 (FIG. 2D). In a second variant, the order of magnitudedifference is maintained throughout junction depth “Xj” of doped region138 in wafer 105/106, e.g. throughout depth of 0.3 microns. In a thirdvariant, the order of magnitude difference is maintained throughout apredetermined fraction (e.g. ½) of the junction depth Xj.

In an alternative embodiment, a significant number (e.g. greater than10%) of charge carriers are measurement-related carriers (of the typedescribed above) that are created by incidence of probe beam 152. Suchmeasurement-related carriers bias the junction, and a signal ismeasured, for different powers of probe beam 152. A second ordercoefficient of the function is used to determine a property (such asabruptness) of wafer 104/105/106.

As noted above, depending on the wavelength, probe beam 152 generatesmeasurement-related carriers, that in turn bias the junction. Oneembodiment uses the measurement-related carriers to determine abruptnessor other properties as follows. Specifically, measurements of theintensity of probe beam 152 are made as described in reference to act142 of FIG. 2A, except that multiple measurements are made for differentpowers of probe beam 152. When making the measurements, the intensity ofgeneration beam 151 is kept at a constant amplitude of modulation (e.g.25 mA). The constant modulation amplitude is selected to be at a lowerend of a range (in which the amplitude is normally varied to generate apower curve), because abruptness induced effects are more exaggerated atlow powers. At low powers of generation beam 151, the effects caused byother than abruptness are minimized, so that abruptness can be measuredby varying the intensity of probe beam 152.

In this embodiment, a power curve need not be in fact generated, but ameasure of its slope is obtained, because modulation of generation beam151 results in the measured signal being indicative of slope of thepower curve. Specifically, the signal being measured is due tointereference of two portions of probe beam 152 that are modulated andthat are reflected from a front surface of the wafer, and from ajunction, as described elsewhere herein. After a first measurement, theprobe beam's intensity is changed, and the signal is measured again, toobtain a second measurement.

A difference between the two measurements is an indicator of abruptness(e.g. varies linearly as abruptness) because at different powers of theprobe beam the interference signal comes from different depths. So, thejust-described procedure is repeated (e.g. on another wafer or onanother die in the wafer), for process control (e.g. a fabricationparameter related to abruptness is adjusted if the difference betweenmeasurements on one wafer is not same as the corresponding difference onanother wafer). Note that although the just-described embodiment usesonly two measurements on each wafer, in other embodiments, additionalmeasurements may be made (at different powers of the probe beam).

Another embodiment modulates both probe beam 152 and generation beam151, at frequencies that differ from one another. Therefore, both theprobe beam and the generation beam are modulating the number of chargecarriers at the junction. The width of the depletion region of thejunction is a non-linear function of the modulation. Hence, a reflectionsignal from the junction appears at the sum and difference frequencies.Therefore, the apparatus makes measurements as described above, butlooks for a signal at the sum or difference in frequencies of modulationof the two beams. Since the mixing in the measured signal is caused by anon-linear response, this is the equivalent of measuring the quadraticand higher fit coefficients (such as cubic and quartic) of a power curvefunction. The measured signal is a function of both depth andabruptness. Such a signal is therefore plotted and analyzed just like apower curve generated with zero modulation of the probe beam.

Regardless of the different ways in which measurements are performed onwafer 104/105/106, the measurements are used (in an operation 160illustrated in FIG. 2A) to determine one or more coefficients, such asthe zeroth order, first order, and/or second order coefficients of afunction that describes the measurements. In one embodiment, two or moreof the reflectance measurements made in act 143/144 (FIG. 2A) are usedto measure a material property of wafer 104/105/106.

Specifically, in act 161 (FIG. 2J), profiler 103 fits the reflectancemeasurements to a line, such as curved line 181 (FIG. 3A). Curved line181 is a plot (along the y axis) of the intensity of the component ofprobe beam 152 appearing at the modulation frequency of generation beam151 (FIG. 2D) after reflection by region 128, as a function of theparameter being varied (along the x axis), e.g. power of generation beam151 incident on region 128. Profiler 103 (FIG. 1A) uses points 181A-181Nobtained by each of the intensity measurements to fit a curved line 181(FIG. 3A) for a wafer (e.g. by connecting points 181A-181N with linesegments).

Next, in act 162 (FIG. 2J), profiler 103 determines one or moreattributes that describe curved line 181, e.g., determines the firstorder coefficient (also called “slope”) and the zeroth order coefficient(also called “intercept”) of one or more straight lines that approximatevarious portions (e.g. two portions described below) of curved line 181,and/or determines an inflection point (e.g. a point at which a second orhigher order derivative becomes zero). In alternative implementations,instead of using straight lines, computer 103C uses quadratic or higherorder functions that approximate curved line 181, e.g. to obtain threeor more such coefficients.

In one such alternative implementation, programmed computer 103Cgenerates a number of curved lines 181-183 (FIG. 3A) from intensitymeasurements on the respective wafers. Specifically, FIG. 3A illustratesmeasurements plotted in a graph with the y axis representing themeasured intensity and the x axis representing the power of generationbeam 151. For example, profiler 103 obtains a number of measurements181A-181N (FIG. 3A) with beams 151 and 152 coincident in the same region128 (FIG. 2D) by changing the power of the generation beam 151. Theintensity measured is of interference between a portion of beam 152reflected by the front surface 153 and another portion of beam 152reflected by the charge carriers that is modulated in phase withmodulation of beam 151. This is the signal plotted on the vertical scaleof the graph in FIG. 3A.

Thereafter, computer 103C uses the measurements to determine curved line181 and/or its coefficients (e.g. curvature). In FIG. 3A, lines 181-183were determined from measurements made over a range of 80 mW power, forthe following wafers (not shown) that were boron doped using a chemicalvapor deposition method to form a shallow layer (on the order of 10 nm):(1) a first wafer that was measured directly after deposition, (2) asecond wafer that was spike annealed to a maximum temperature of 750°C., and (3) a third wafer that was spike annealed to a maximumtemperature of 800° C. In spike annealing, a wafer is heated at a fastramp rate, for example, 100° C./second to a maximum temperature andimmediately ramped down in temperature at a similar rate. Note that nonormalization was done to determine lines 181 -182 of FIG. 3A, althoughthe measurements used in other embodiments may be normalized.

As seen from FIG. 3A, the quadratic coefficient for lines 181-182 (alsocalled “curvature”) varies as a function of the abruptness of thejunction. Specifically, the quadratic term becomes increasingly negativeas the profile becomes increasingly abrupt across lines 181-182. Thesecond wafer with an higher temperature anneal is expected to have lessabruptness because the junction forming dopant atoms diffuse, and asillustrated by line 182 has less curvature than line 183 whichrepresents an as-grown wafer. The lowest abruptness is expected in thefirst wafer since it has been annealed at the highest temperature,causing the greatest diffusion.

In one implementation, the properties and process conditions of wafersrepresented by lines 181-182 are known (as these wafers are ‘referencewafers’), and such properties are plotted as functions of one or more ofthe above-described coefficients, e.g. second order coefficient (alongthe y axis) is illustrated in FIG. 3B as a function of annealtemperature. Thereafter, the corresponding coefficient of a newlyfabricated wafer is used to look up the respective properties and/orprocessing conditions.

Specifically, in the example illustrated in FIG. 3A, curved lines181-182 have the following fit coefficients, anneal temperature andabruptness, as shown in Table 1. TABLE 1 Abruptness Zeroth- First-Second- Anneal Temperature in nanometers/ Line order order order DegreesCentigrade decade 183 −56.1 210.63 −.414 800 3.50 182 −111.4 244.5 .674750 2.98 181 86.79 307.28 −.766 As-grown 2.71Abruptness is measured in units of nanometers/decade which is thedistance in nanometers over which the concentration of dopants drops bya factor of 10. For example, if the concentration drops from 10¹⁹atoms/cm³ to 10¹⁸ atoms/cm³ in a distance of 2.5 nm, then abruptness is2.5 nm/decade.

In one example, computer 103C uses the second order coefficient of value−0.674 as illustrated in FIG. 4 to obtain the abruptness of 2.98nm/decade. In the above-described example of the wafer represented bycurved line 183, programmed computer 103C compares the measured value of2.98 nm/decade to the specification of 2.8 nm/decade, and identifies thewafer as being rejected (e.g. by moving the wafer into a bin of rejectedwafers), and thereafter adjusts a process parameter e.g. drives a signalon line 108 (FIG. 1A) to reduce the temperature by 25° C.

Instead of, or in addition to determining a process condition (e.g.anneal temperature as described above), the above-described attributesderived from the intensity measurements can be used to determineabruptness of the semiconductor material in illuminated region 128.Specifically, profiler 103 uses the curvature to determine junctionabruptness by looking up a graph (FIG. 3B) of such curvatures plottedagainst abruptness of wafers having known properties. In theabove-described example, the second order coefficient yields abruptnessof nanometers per decade through direct use of a correlation graph suchas FIG. 3B.

Thereafter, profiler 103 compares the value of for example, 2.8nanometers/decade with a predetermined range of acceptable abruptnesse.g. the range of 2.7 to 2.9 nm/decade. As the value of 2.8 falls withinthe range, wafer 105/106 is identified as acceptable, and is processedfurther in the normal manner (as illustrated by act 262 in FIG. 2A). Ifthe measured junction depth falls outside the predetermined range, wafer105/106 is rejected (as illustrated by act 260 in FIG. 2A), and one ormore process conditions are adjusted e.g. by adjusting the addition ofdopants (as illustrated in act 263).

Note that the above-described coefficients can be extracted from therespective measurements using any curve-fitting method well known in theart. For example, a “least squares” fit may be performed, to minimizethe mean squared deviation between a function and the measurements.Assuming the measurements form a matrix (S_(i), P_(i)), where the i^(th)signal is measured in response to the i^(th) power, the mean squareddeviation MSD is given by the following equation.MSD=Σ [S _(i) −f(P _(i))]²

To find a minimum MSD, a quadratic function f(P_(i))=a+bP_(i)+cP_(i) ²is fitted to the measurements, to determine coefficients a, b and c,e.g. by taking the partial derivative of MSD with respect to a, b and cand setting these to zero. Such methods are well known and implementedin standard curve-fitting routines, such as those found in MicrosoftExcel which provides a “trendline” option to automatically fitcoefficients. Alternatively, a, b and c can be found using a matrixsolver in a program such as Mathcad, or custom routines may be writtenand embedded within user interface or data analysis software associatedwith the measurement system.

In one embodiment, a quadratic function fits the measurements to a highdegree of accuracy (e.g. to within 10%), so that it is not necessary touse higher order terms or fit functions other than power series.However, fits to higher order terms of a power series may be performed,e.g. to increase accuracy in the abruptness measurement, or in otherembodiments other functions may be fit to the measurements, to extractabruptness from fit coefficients, as would be apparent to the skilledartisan.

One or more of these coefficients are used (see act 172 in FIG. 2A) todetermine if wafer 104/105/106 conforms to the specification for suchwafers, e.g. curvature below a predetermined limit. If wafer 106conforms to the specifications, wafer 106 is identified (see act 173 inFIG. 2A) as acceptable (e.g. by movement in the direction for furtherprocessing) and the conditions in wafer processing unit 101 (FIG. 1A)and in rapid thermal annealer 102 are left undisturbed. Thereafter, theabove-described acts are repeated on another wafer or after furtherprocessing on the same wafer.

If a wafer 106 does not conform to the specifications, wafer 106 isidentified as unacceptable (e.g. discarded) and optionally profiler 103is used (in act 174 in FIG. 2A) to adjust (either automatically or undermanual control) (1) the conditions (e.g. dosage of dopants) in unit 101by driving a signal on a line 107 (FIG. 1A), or (2) the conditions (e.g.annealing temperature) in annealer 102 by driving a signal on line 108,or both. Then the above-described acts are again repeated.

Note that the adjustment of a process condition can also be performedeven when a wafer is accepted (as illustrated by act 173 in FIG. 2A),e.g. if the abruptness falls close to the limits of a predeterminedrange, e.g. within 5 percent of a limit. As noted above, to adjust theprocess condition, profiler 103 provides a signal to either or both ofunit 101 and annealer 102 to return the value of the abruptness into themiddle of the predetermined range.

As described herein, the measurement performed by profiler 103 isnon-destructive, is performed in a few square microns, and can beperformed in a relatively short time (e.g. five seconds in one region or50 seconds at 10 regions over a wafer). Measuring a property of annealedwafer 106 during (or immediately after) fabrication as described hereinincreases yield, as compared to an off-line measurement of a testwafer's properties.

Note that instead of directly using the second order coefficient, thecoefficient can be interpolated (as illustrated in act 171 illustratedin FIG. 2J) with respect to coefficients of wafers having known junctionabruptness, to identify abruptness of wafer 104/105/106. For example,the second order coefficient for wafer 104/105/106 is compared withcorresponding coefficient values of wafers (also called “referencewafers”) that have known abruptness, to find the two closest coefficientvalues, and a linear interpolation between the corresponding abruptnessvalues yields abruptness of wafer 104/105/106. Instead of linearinterpolation, a curve may be fitted to relate different coefficientvalues to the respective abruptness values, and the curve (see FIG. 4)is then used to find abruptness of wafer 104/105/106.

Abruptness of reference wafers can be determined (see act 110 in FIG.2A) in any manner well known in the art, such as spreading resistanceprofile (SRP)) or by Secondary Ion Mass Spectrometry (SIMS). Also,instead of using an empirical method to determine properties ofreference wafers, simulation may be used. In one implementation,software in computer 103C compares a simulated power curve with acorresponding curve (see curve 181 in FIG. 3A) obtained by measurementof an interference signal (amplitude and phase, wherein phase is used todetermine a sign to be used with the amplitude) as a function of thepower of generation beam 151. Specifically, to find curvature for awafer being tested, the software compares the measured power curve to anumber of preexisting power curves that have been obtained by simulation(e.g. by use of the simulators Atlas and Athena, both available fromSilvaco International, Santa Clara, Calif.). The matched curvatureobtained by simulation determines the abruptness.

In one implementation, the abruptness (or the second order coefficientitself, depending on the embodiment) of wafers undergoing the samefabrication process, if smaller than or equal to a predetermined limitidentify acceptable wafers. For example, if abruptness of wafer 105/106is greater than or less than a maximum limit or a minimum limitrespectively, wafer 1015/106 is identified as unacceptable (e.g. byplacing in a bin of rejected wafers). In one implementation, computer103C displays on monitor 103M a message indicating that measurementsidentify a wafer 104/105/106 as unacceptable, while in anotherimplementation computer 103C drives a signal to a robot (not shown) tomove wafer 104/105/106 into a bin of rejected wafers (if rejected). Theacceptable wafers are processed further in the normal manner (see act262 in FIG. 2A).

In some embodiments, a maximum limit on abruptness is set empirically bycomparing the above-described abruptness of one or more reference wafers(wherein the reference wafers are known to be good or bad based onelectrical tests for conformance to the specification for such wafers),thereby to identify a maximum limit on the abruptness for acceptablewafers. The empirical method used can be any method such as one of themethods described in “STATISTICAL QUALITY CONTROL HANDBOOK” availablefrom AT&T Technologies, Commercial Sales Clerk, Select Code 700-444,P.O. Box 19901, Indianapolis, Ind. 46219, phone 1-800-432-6600, secondedition, 1958.

Specifically, the variations in such abruptness are correlated with theperformance of a reference wafer during electrical tests that identifyreference wafers (that are good). In one example, four different wafershave 1%, 5%, 10% and 20% variation from abruptness of an epitaxialwafer, and have the respective variations in performance speed of 8%,10%, 20% and 25% during electrical testing of integrated circuit diesformed from the respective wafers.

Assuming that 10% and greater variation in speed is unacceptable, amaximum limit is set for this example at 5% variation. Therefore, allwafers having abruptness lower than 5% from the maximum limit areidentified as acceptable wafers (as illustrated by act 173 in FIG. 2A).Note that if the abruptness of a number of wafers that have beensuccessively processed are close to the maximum limit (e.g. all greaterthan 4.5% in the just-described example), one or more parameters used inprocessing the wafers may be adjusted (e.g. as described herein inreference to act 174 of FIG. 2A) even though none of the wafers arediscarded.

In another implementation, instead of determining abruptness in onelocation and comparing the abruptness to a predetermined limit,abruptness values at multiple locations are plotted, e.g. values along aline are plotted in a graph, to form a “linear” scan. In addition,operation 140 is used in one implementation to screen out startingwafers formed of bare silicon with an epitaxial layer grown by ChemicalVapor Deposition (CVD) used for the start of the process (e.g. startingwafers with thin epitaxial layers, to measure the depth and abruptnessof the epitaxial layers).

Anneals are typically done by heating the wafer rapidly with lamps (notshown) in annealer 102 (FIG. 1A). The illumination by the lamps inannealer 102 may not be uniform, and the amount of heat that enters apatterned wafer 105 at any point may be a function of the thickness ofdielectric layers (such as silicon dioxide or silicon nitride to beformed on surface 153), and the integrated circuit pattern therein.Specifically, the different layers (not shown) in wafer 105 reflectdifferent amounts of power, thereby causing variations in the amount ofheating of wafer 105.

Thus annealing of implanted wafer 105 may not be uniform, and thecharacteristics of a junction (formed at an interface between dopedregion 138 and semiconductor material 156 in FIG. 2D at a depth xj fromsurface 153) in annealed wafer 106 may vary from point-to-point. Lines181-183 (FIG. 3A) indicate to a person skilled in semiconductor physicsthe variations injunction abruptness on a micron and sub-micron scale.Therefore, such lines are used by a human operator of profiler 103 tocheck if the just-formed transistors are uniform all across wafer105/106, and to conform to specifications (e.g. by adjusting the anneal,implant or circuitry design) the transistors in a to-be-formed wafer.

Instead of a human operator, such checking is automated by computer 103Cin another embodiment. For example, instead of forming a display (notshown), computer 103C (1) automatically uses the abruptness values fromeach wafer to compute the mean and standard deviation values, over alarge number of wafers (typically several hundred or more), and (2)automatically uses these values of mean and standard deviation toidentify when an implant or anneal process is out of specification,using statistical process control methods that generate controlparameters (as described in pages 5-30 of the above-referenced book fromAT&T Technologies, and these pages are incorporated by reference herein)to be provided to unit 101 or annealer 102.

As noted above, although a linear scan is discussed above, an area scanis performed in another embodiment. Specifically, profiler 103 (FIG. 1A)performs a number of reflectance measurements in a corresponding numberof regions (e.g. by repeating acts 140-160 in FIG. 1B) in a closelyspaced grid (e.g. a grid that divides a wafer 105/106 into a number ofregions, each region having an area 10 microns by 10 microns). Themeasurements are plotted to form on monitor 103M (FIG. 1A) a graph ofthe measured intensity vs. x-y position (e.g. in the form of varioustypes of hatched regions or as a three dimensional image).

Therefore in the just-described embodiment, profiler 103 functions as ascanning abruptness microscope that displays on monitor 103M theabruptness of various regions on wafer 104/105/106, and can be used in amanner similar to the use of a scanning electron microscope. In oneexample, four hundred measurements are taken in an area of 100 μm×100 μmand displayed in a three dimensional graph wherein the x and y axesdefine, in the two dimensions, a region on patterned wafer 105, and thehatch pattern (that is displayed on monitor 103M in a third dimension)indicates the measured abruptness. Such a graph (not shown) of the areascan is used by an engineer skilled in semiconductor physics to evaluatewafer 105/106, in a manner similar to the use of a scanning electronmicroscope. As noted above, instead of plotting a graph to be manuallychecked, the abruptness measurements are checked automatically.

If necessary, profiler 103 can move beams 151 and 152 relative to oneanother at any time (e.g. before, during or after identifying a wafer asaccepted/rejected as shown by act 170 in FIG. 2A), although in oneembodiment the distance between beams 151 and 152 is set initially andthereafter kept fixed for all measurements. Beams 151 and 152 may beinitially arranged to be concentric and/or overlapping, ornonoverlapping (depending on the implementation) by appropriatelyadjusting the separation distance during setup. In such an embodiment,no measurements of the type described herein are made during the setupphase, and when such measurements are made after the setup phase, theseparation distance is left unchanged.

In one embodiment, profiler 103 includes two piezoelectric actuatorsthat control the positions of beams 151 and 152. Specifically, theactuators (not shown) move a collimating lens of a laser that generatesprobe beam 152 along each of two orthogonal axes x, y that are bothperpendicular to axis 155 of generation beam 151, thereby shifting theposition of probe beam 152 relative to generation beam 151.

Profiler 103 may align beams 151 and 152 to be coincident in thefollowing manner. Specifically, profiler 103 repeatedly moves probe beam152 relative to probe beam 151 along an axis (e.g. along x axis), asillustrated in FIGS. 2G and 2H and obtains an intensity measurementsafter each movement. In one embodiment, the measurements are made aspart of a setup phase, and profiler 103 does not process themeasurements between movements to determine material property). In analternative embodiment, such measurements are processed to determine amaterial property, while profiler 103 avoids generation of a wave ofcharge carriers, by using a sufficiently low modulation frequency asdescribed elsewhere herein.

After making the measurements, profiler 103 optionally plots themeasurements as a function of the relative position as illustrated inFIG. 2E, and determines the position (in this embodiment the voltageapplied to the piezoelectric actuator) at which the intensitymeasurement is at a maximum, e.g. 25 mV volts in FIG. 2E. In oneembodiment, profiler 103 moves probe beam 152 relative to generationbeam 151 in a first direction (e.g. along the positive x axis) by anincremental distance Δx (e.g. 0.1 μm), measures if the measuredintensity is larger than the largest intensity so far, and if so, savesthe voltage signal that was used to maintain the current total distancebetween beams 151 and 152 and also saves the measured intensity as thelargest intensity. Thereafter, profiler 103 repeats the just-describedprocedure, until the total distance between beams 151 and 152 reaches orexceeds a predetermined distance, e.g. ½ of the diameter of the largerof beams 151 and 152, wherein the incremental distance Δx is {fraction(1/10)} of the larger diameter.

Next, profiler 103 moves probe beam 152 relative to generation beam 151in a second direction (e.g. along the negative x axis) that is oppositeto the first direction (e.g. positive x axis), and performsabove-described procedure. Profiler 103 treats the first and seconddirection (negative and positive x axis) travel to be a continuum, andso obtains the voltage signal of 25 μvolts (FIG. 2E) corresponding tothe maximum intensity measurement along one axis (e.g. along x axis).Similarly, profiler 103 moves probe beam 152 relative to generation beam151 along another axis (e.g. y axis) that is orthogonal to thejust-described movement, and once again determines the voltage appliedto the piezoelectric actuator at which the intensity measurement ismaximum, e.g. 40μ volts in FIG. 2F. Therefore, profiler 103automatically positions beams 151 and 152, e.g. to be coincident or tohave a predetermined separation distance.

Graphs, such as line 191 (FIG. 3B), used to determine a materialproperty or a process condition are generated in one of the twofollowing ways (in two different embodiments). In the first embodiment,a set of wafers (also called “reference wafers”) is selected or preparedto have a range of material properties (by varying process conditions,such as implant energy, dose or anneal temperature), and thereafterprofiler 103 is used to obtain intensity measurements and generate fitcoefficients or other attributes for power curves of each of thereference wafers (as described above). Thereafter, the fit coefficientsor attributes are used to plot graphs, such as line 191. In a secondembodiment, a number of wafers (also called “reference wafers”) aresubjected to intensity measurements in profiler 103 (as describedabove), followed by use of a conventional measurement technique, such asSIMS to determine the actual doping profile therein.

Therefore, after one or more of the above-described graphs (see FIG. 3B)are prepared, the abruptness of a wafer under fabrication is determinedby the above-described method 200 (FIG. 2A) without the need to destroythe wafer, because profiler 103 simply uses the above-described graphsto generate measurements of abruptness. Therefore, profiler 103eliminates the cost associated with test wafers otherwise required bythe prior art method.

Although in the above description, computer 103C has been described asperforming various computations for preparation of lines (e.g. line 181in FIG. 3A) used to measure material properties, such graphs can beprepared by another computer, or alternatively can be prepared manuallyby performing the above-described acts. Moreover, although in oneembodiment the above-described lines (e.g. FIG. 3B) are prepared, inanother embodiment such graphs are not prepared and instead thereflectance measurements are simply used to perform the various acts ofmethod 200 by use of equations related to such graphs. For example,instead of drawing a line 181 (FIG. 3A), the curvature of such a line isdetermined, and thereafter a predetermined function (which may bedetermined from test wafers) that maps the curvature to abruptness isused to identify abruptness. Alternatively, curvature itself is reporteddirectly.

Curvature is measured in one embodiment, for instance, by measuring thedifference in signal between three points 181A-181N on a power curve 181(FIG. 3A). Points 181A-181N may be spaced close to one another, e.g.with a 1% difference in powers of generation beam 151. In an alternativeembodiment, curvature is measured by measuring the signal using anamplitude modulation of the generation laser with the average powerlevel set at some measurement value, for instance, average power at 60mW and modulation of ±1 mW reports the slope of the power curve, whenthe power of the generation beam is at 60 mW (e.g. based on measurementsat 61 mW and 59 mW). Similarly, measurement at another power, say 62 mWwith the ±1 mW modulation measures another slope. The change in slope isthe curvature of the power curve.

In one implementation, beam 152 (FIG. 1C) is a laser beam having awavelength greater than 1 μm (the wavelength at which photons haveapproximately the same energy as the bandgap energy of silicon). Notethat the wavelength of beam 152 depends on the bandgap energy andtherefore on the specific material in wafer 105/106, and is differentfor germanium.

In one embodiment wherein a portion of probe beam 152 reflected by frontsurface 153 (FIG. 2D) interferes with another portion reflected byexcess carriers, probe beam 152 is generated by a laser 501 (FIG. 4),that can be a conventional laser diode, such as a 980 mm wavelengthInGaAs diode with a maximum power of 70 mW made by Spectra Diode Labs,San Jose, Calif.

In a second embodiment wherein probe beam 152 is interfered with a phasevariable beam, laser 501 is a distributed Bragg reflector (DBR) AlGaAslaser with a wavelength of 1083 nm and a power of 50 mW (Spectra DiodeLabs, San Jose, Calif.).

A DBR laser is used in the second embodiment because it has a coherencelength in excess of a meter. This simplifies interferometer design,since the reference beam length is not critical as long as thedifference in path length between the reference beam path and the probebeam path is shorter than the coherence length (the probe beam pathlength is twice the distance from beam splitter 512 to the wafer 516;the reference beam path length is twice the distance from beam splitter512 to mirror 513). The output of laser 501 is collimated using lens 502to provide a collimated beam 503 with a diameter of 3 mm. Lens 502 canbe, for example, part number WT-CY3-163-10B-0.5 available from WaveOptics, Mountain View, Calif.

However, in one embodiment wherein interference is between reflectionfrom the junction and the front surface, the coherence length need onlybe on the order of a micron (e.g. less than 10 microns)—that is thecoherence length must be on the order of the path length difference,which is twice the junction depth in this embodiment.

In one embodiment, a generation beam 151 is created by an above bandgaplaser 505, such as an AlGaAs diode laser with a wavelength of 830 nm andpower of 200 mW, available from Spectra Diode Labs, San Jose, Calif.Profiler 103 includes a lens 507, which is part number 06GLC002/810available from Milles Griot Corporation, Irvine, Calif. Lens 507collimates the beam from laser 505 to generate a collimated beam 151with a diameter of 3 mm. Lens 507 is mounted on a positioner (not shown)for providing motion to beam 151 with respect to beam 152.

The relation between wavelengths of beams 151 and 152 produced by lasers501 and 505 is a critical aspect in one embodiment and leads tounexpected results, for example when beam 151 contains photons havingenergy above silicon's bandgap energy and beam 152 contains photonshaving energy approximately the same as or less than the bandgap energy.In this example, for a silicon wafer the 830 nm and 1083 nm wavelengthbeams provide one or more benefits described herein.

Wavelength 830 nm is considered particularly suitable for generationbeam 151 of this example, because the absorption length in silicon isabout 15 microns. Thus, the absorption length is much greater than thejunction depth, and creation of excess charge carriers is nearly uniformover the depth of concern in the measurement. Because the photon energyis close to the bandgap energy, photon generation is more efficient,with less energy going directly into heating the semiconductor.

Also, the absorption length at wavelength 980 nm is about 250 microns,and therefore the number of excess carriers being created by such aprobe beam 152 is sufficiently low to ensure minimum perturbation to theexcess carrier distribution. Moreover, the absorption length atwavelength 980 is short enough that very little reflection from a backsurface of the wafer is seen (wafers are typically 600-800 micronsthick), since the back surface reflection can potentially cause spurioussignals.

Note that silicon has a broad band edge (in contrast to direct bandgapmaterials such as GaAs, which have a sharply defined bandgap energy). Aprobe beam 152 with wavelength of 980 nm provides photons of energywithin this broad band edge, giving rise to the long absorption length,to minimize carrier generation due to probe beam 152, but also providingsufficient absorption to attenuate beam 152 so that reflections from theback side of the wafer are not seen. For this reason, a probe beam 152of wavelength of 980 nm is used in this example when inspecting dopedjunctions in substrates of low doping concentration (on the order of10¹⁵ dopant atoms per cubic centimeter), where optical absorption due tothe presence of free carriers is low.

Beams 151 and 152 are combined using dichroic splitter 510 (such as apartially transmissive mirror (e.g. part number 1918-b available fromDominar of Santa Clara, Calif.), forming a superposed beam 511. Beam 511passes through a 50:50 beam splitter 512 (e.g. part number 2005 fromDominar ) that directs a portion of beam 511 to detectors 522 a and 522b (via filter 520 and polarizing beam splitter 521), for use inmeasurement of an interference signal. The remainder of beam 511 passesthrough a 90:10 beam splitter 514 (available from Precision AppliedProducts of Fullerton, Calif., by specifying 93.3% transmission at 0.83microns wavelength and 90% transmission at 0.980 microns wavelength),and an objective lens 515 (such as a 100×, 0.8 NA lens made by Olympusof Tokyo Japan). Objective lens 515 focuses the combined beam 511 ontowafer 516.

The specifications for beam splitter 514 are selected based on thewavelengths of the generation and probe beams to ensure that a majorityof the power is transmitted and a smaller amount (e.g. 10%) of the poweris reflected. Note also that probe beam 152 is focused only in a carriercreation region 128 (FIG. 2D) that is formed by focusing generation beam151 (FIG. 4).

Specifically, because of chromatic aberration, the focal planes of beams151 and 152 differ slightly. The size of the focal spot for probe beam152 is smaller than the size of the focal spot for generation beam 151by virtue of the shorter wavelength of beam 151. If wafer 516 is placedin the focal plane of beam 152, beam 151 will be slightly out of focusand its spot on front surface 153 (FIG. 2D) of wafer 516 (FIG. 4) willbe larger in diameter and fully overlay the focal spot of beam 152.

This effect of the spot of beam 151 overlaying the spot of beam 152 canalso be achieved by underfilling the objective lens 515 with thegeneration beam 151, by making the generation beam 151 diameter at theentry to objective lens 515 smaller than the entrance aperture of lens515, thereby increasing the generation beam spot size.

Light reflected from wafer 516 passes back through objective lens 515,90:10 beam splitter 514, and into 50:50 beam splitter 512. Half of thelight reaching beam splitter 512 is directed back through filter 520(which is a bandpass filter that blocks the light from beam 151 butpasses the light from beam 152). Filter 520 can be, for example, Schottglass RG830, available from Spindler & Hoyer Corporation of Goettingen,Germany. Alternately, filter 520 can be a narrow-band pass filter with acenter wavelength of 1080 nm, available from Melles Griot of Irvine,Calif.

Filter 520 removes photons of generation beam 151 from the reflectedbeam, thereby allowing detector 522 a to see only the photons of probebeam 152. Filter 520 is a critical component in one embodiment andprovides the unexpected result of eliminating feed-through of themodulated signal (generated by beam 151) to detector 522 a that wouldotherwise be present when using a prior art system. In this particularimplementation, germanium may be used in photo detector 522 a to providesensitivity to photons of wavelength 1083 nanometers that are generatedby laser 501. Alternatively, either a germanium or a siliconphotodetector may be used in the first embodiment, which uses a probelaser wavelength of 980 nm.

In some embodiments, a reference beam is formed by a portion of probebeam 152 that reflects from front surface 153 (FIG. 2D), and 50:50 beamsplitter 512 diverts 50% of the reflected beam from front surface 153toward detector 522 a. Note that in the first embodiment, beam splitter521, detector 522 b, and amplifier 523 b are not used (i.e. are notpresent).

Detector 522 a is a photocell (such as a photodiode or aphototransistor, e.g. J16-8SP-RO5M-HS from EG&G Judson ofMontgomeryville, Pa., USA) that converts the incident interferencesignal into a current. Amplifier 523 a converts the current to anamplified current which is then sent to an amplifier 524 that in turn iscoupled to a lock-in amplifier 525 (such as model 830 available fromStanford Research Systems, Sunnyvale, Calif.).

Lock-in amplifier 525 includes a reference oscillator at the lock-indetection frequency. This oscillator is coupled to a laser driver 526 toprovide a signal to laser 505 that is modulated at the same frequency asthe signal provided by lock-in amplifier 525. Lock-in amplifier 525provides a signal indicating the amplitude as well as phase of reflectedbeam with respect to modulation by laser driver 526 to a processor 527,such as a personal computer running software to capture and display thesignal in an appropriate manner (e.g. in a graph). The signal may alsobe stored in the personal computer (e.g. in a database on the hard disk)for later processing.

In one implementation, personal computer 527 has a line 528 that iscoupled to lines 107 and 108 (described herein in reference to FIG. 1A)thereby to control the acts performed by ion implanter 101 and rapidthermal annealer 102 based on measurement of one or more materialproperties as described herein.

Beam splitter 514 diverts 10% of the return beam from wafer 516 via alens 517 (such as tube lens 81845 available from—Nikon of Tokyo, Japan)to a camera 518 (such as a CCD camera, e.g. model 85400 available fromFJW Industries of Palatine, Ill.). The signal provided by camera 518 isfed into a vision system (not shown in FIG. 4), such as modelASP-60CR-11-S available from Cognex Corporation, Boston, Mass.

Positioning of wafer 516 with respect to the combined beam 511 isaccomplished using a microscope that includes stage 529, objective lens515, beam splitter 514, lens 517 and camera 518. Stage 529 is used tomove wafer 106 relative to beam 511 in the X, Y and Z directions.Specifically, stage 529 can be used to move wafer 516 in the verticaldirection along the Z axis to adjust focus, and in a horizontal plane toadjust the position of region 120 of FIG. 1E relative to beam 511.

Numerous modifications and adaptations of the above-describedembodiments, implementations, and examples will become apparent to aperson skilled in the art of semiconductor physics. For example,although computer 103C is described as being programmed with one or morespecific equations, computer 103C can be programmed with other equationsdescribed herein, or with one or more equations that approximatelydetermine abruptness, for use with measurements performed by profiler103 while creating a diffusive modulation of charge carriers in a waferunder measurement.

As another example, an approximate equation used by profiler 103 tomeasure abruptness can be obtained by curve-fitting to measurement datafrom reference wafers, or by curve-fitting to data obtained from anumerical model, or both depending on the specific implementation.

Moreover, other embodiments may use a function other than a power seriesas a fit function for the power curve, such as an exponential ortrigonometric series, where linear and quadratic terms do not exist, butfit coefficients are used to determine the shape of the power curve, andabruptness or other material properties are determined from suchcoefficients.

Note that the quadratic (or other higher order) terms of a power seriesfunction that fits the power curve may depend on both depth andabruptness. In one implementation, there are two unknowns (depth andabruptness) and two coefficients (first order and second order). In thisimplementation, the linear term is primarily a function of depth and thequadratic a function of both depth and abruptness. Therefore, the linearcoefficient is used to find the depth and the quadratic coefficient tofind the abruptness with knowledge of the depth.

Also, the coefficients of a function that describes the power curve areused in one embodiment to extract material properties other thanabruptness, such as doping concentration. Also, power curves for variousvalues of a parameter other than the probe beam power can be used toevaluate a semiconductor wafer, e.g. the parameter can be modulationfrequency, or spot size or separation distance.

Therefore, numerous such modifications and adaptations of theabove-described embodiments are encompassed by the attached claims

1-43. (canceled)
 44. A method for evaluating a wafer, said methodcomprising: measuring an intensity of a portion of a beam reflected bysaid wafer; changing a parameter related to charge carriers in saidwafer and repeating said measuring to obtain a plurality of measurementsfor a corresponding plurality of values of said parameter; computing acoefficient of a function that relates said measurements to said values;and using said coefficient to control fabrication of another wafer. 45.The method of claim 44 wherein: the function includes a power series;and the coefficient is for a constant in said power series.
 46. Themethod of claim 44 wherein: the function includes a power series; andthe coefficient is for a linear term in said power series.
 47. Themethod of claim 44 wherein: the function includes a power series; andthe coefficient is for a quadratic term in said power series.
 48. Themethod of claim 44 wherein: the number of said charge carriers ismodulated at a frequency that is sufficiently low to avoid creation of awave in space of said charge carriers; and the method includes usingsaid frequency to identify said intensity during said measuring, saidportion being modulated at said frequency.
 49. The method of claim 48wherein: the parameter is diameter of a beam incident on said wafer tocreate at least a plurality of said charge carriers.
 50. The method ofclaim 44 wherein said coefficient identifies a property of said wafer,and the method further comprising: measuring said property in said waferusing secondary ion mass spectrometry (SIMS); and calibrating said valuedetermined by said computer against a measurement obtained by SIMS. 51.The method of claim 44 wherein said coefficient identifies a property ofsaid wafer, and the method further comprising: measuring said propertyin said wafer using another method; and calibrating said valuedetermined by said computer against a measurement obtained by saidanother method.
 52. The method of claim 44 wherein: said property isabruptness of a junction in said wafer.
 53. The method of claim 44wherein: said beam is hereinafter “second beam”; said method includesfocusing a first beam on said wafer, photons of said first beam havingenergy greater than bandgap energy of semiconductor material in saidwafer; and photons of said second beam having energy sufficiently lowerthan said energy of photons of said first beam to avoid creation of morethan a negligible number of charge carriers in said wafer when saidsecond beam is incident on said wafer.
 54. The method of claim 53wherein: the parameter is power of said first beam; and storing inmemory the plurality of values of said coefficient for a correspondingplurality of power levels.
 55. The method of claim 44 wherein saidmeasuring comprises: interfering a reflected portion of said beam withan unreflected portion of said beam to obtain a sum component and adifference component; and determining a difference between a firstmagnitude of said sum component and a second magnitude of saiddifference component.
 56. The method of claim 44 further comprising,prior to said interfering: passing said reflected portion and saidunreflected portion through a filter, said filter blocking the passageof said second beam.
 57. The method of claim 44 wherein: saidfabrication includes annealing said wafer prior to said measuring; andsaid using includes adjusting annealing of another wafer depending onsaid coefficient.
 58. The method of claim 44 wherein: said fabricationincludes forming a doped layer in said wafer prior to said measuring;and said using includes adjusting doping of another wafer depending onsaid coefficient.
 59. The method of claim 44 further comprising:normalizing said values prior to said computing. 60-64. (canceled).